What is expand (x-1)(x-4)(x-1+i)(x-1-i) ?

The solution to expand (x-1)(x-4)(x-1+i)(x-1-i) is x^4-7x^3+16x^2-18x+8

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expand (x-1)(x-4)(x-1+i)(x-1-i)

expand

(x - 1) (x - 4) (x - 1 + i) (x - 1 - i)

x^{4} - 7 x^{3} + 16 x^{2} - 18 x + 8

Solution steps

(x - 1) (x - 4) (x - 1 + i) (x - 1 - i)

Expand

(x - 1) (x - 4) (x - 1 + i) (x - 1 - i) : (x^{2} - 5 x + 4) (x - 1 + i) (x - 1 - i)

= (x^{2} - 5 x + 4) (x - 1 + i) (x - 1 - i)

Expand

(x^{2} - 5 x + 4) (x - 1 + i) : 4 i + x^{3} - 6 x^{2} + x^{2} i + 9 x - 5 x i - 4

= (4 i + x^{3} - 6 x^{2} + x^{2} i + 9 x - 5 x i - 4) (x - 1 - i)

Distribute parentheses

= 4 i x + 4 i (- 1) + 4 i (- i) + x^{3} x + x^{3} (- 1) + x^{3} (- i) - 6 x^{2} x - 6 x^{2} (- 1) - 6 x^{2} (- i) + x^{2} i x + x^{2} i (- 1) + x^{2} i (- i) + 9 xx + 9 x (- 1) + 9 x (- i) - 5 x i x - 5 x i (- 1) - 5 x i (- i) - 4 x - 4 (- 1) - 4 (- i)

Simplify

4 i x + 4 i (- 1) + 4 i (- i) + x^{3} x + x^{3} (- 1) + x^{3} (- i) - 6 x^{2} x - 6 x^{2} (- 1) - 6 x^{2} (- i) + x^{2} i x + x^{2} i (- 1) + x^{2} i (- i) + 9 xx + 9 x (- 1) + 9 x (- i) - 5 x i x - 5 x i (- 1) - 5 x i (- i) - 4 x - 4 (- 1) - 4 (- i) : x^{4} - 7 x^{3} + 16 x^{2} - 18 x + 8

= x^{4} - 7 x^{3} + 16 x^{2} - 18 x + 8

(e^{3 + y} + 5) + (e^{3 + y} + 6) y^{'} (t)

\frac{4 - 64}{20 + \frac{10000}{33 s} + 2 s}

3 (4 x + 15 y = 72)

(e^{3 x} - 1) \cdot (4 - x^{2})

\frac{( x ^{2} )}{( 6 + x ) ^{3}}

What is expand (x-1)(x-4)(x-1+i)(x-1-i) ?
The solution to expand (x-1)(x-4)(x-1+i)(x-1-i) is x^4-7x^3+16x^2-18x+8